They had the super attend to the problem and he didn't do anything that helped and we have paid for a private extermination company to come in. The problem still exists. How long is long enough before we can break the lease. If we do break the lease do we then forfeit our security deposit?

You will have to sue for breach of warranty in order to get the judge to allow you to break the lease. You can withhold rent for your extermination costs. The Landlord will sue you but then you would counterclaim that they breached the warranty of habitability. This is a good resource for you...http://www.ag.ny.gov/sites/default/files/pdfs/publications/Tenant_Rights_2011.pdf